To find the distance traveled by the car at the end of 4.0 seconds, we need to integrate the velocity function with respect to time to obtain the displacement function.
Given: Initial velocity, u = 16 m/s Acceleration, a = -0.50t m/s^2 Time, t = 4.0 s
The velocity function v(t) can be obtained by integrating the acceleration function with respect to time:
v(t) = ∫(-0.50t) dt = -0.25t^2 + C,
where C is the constant of integration.
To determine the constant of integration, we can use the initial condition where v(0) = 16 m/s:
16 = -0.25(0)^2 + C, C = 16.
So, the velocity function becomes: v(t) = -0.25t^2 + 16.
Now, to find the displacement function, we integrate the velocity function with respect to time:
s(t) = ∫(-0.25t^2 + 16) dt = -0.25(t^3/3) + 16t + D,
where D is the constant of integration.
Using the initial condition where s(0) = 0 (assuming the car starts from the origin), we can find the value of D:
0 = -0.25(0^3/3) + 16(0) + D, D = 0.
Thus, the displacement function becomes: s(t) = -0.25(t^3/3) + 16t.
To find the distance traveled at the end of 4.0 seconds, we substitute t = 4.0 s into the displacement function:
s(4.0) = -0.25(4.0^3/3) + 16(4.0), s(4.0) = -21.333 + 64, s(4.0) = 42.667 m.
Therefore, the car has traveled a distance of approximately 42.667 meters at the end of 4.0 seconds.